The aim of this section is to get you to recognize grays, mix them reliably with paints, and use them effectively in design.

neutrals in context

Let's start by putting near neutral colors in context. The defining feature of near neutrals is their chroma or saturation  they don't have any.

Well, almost. Think of chroma as the balance between hue and value. Pure neutral tones contain no information at all about hue: they are achromatic or colorless, and vary only in lightness or value. Strongly chromatic colors are so intense that the color sensation frequently obscures the color value, which weakens the clarity of the value structure.

Saturation or chroma is a measure of the balance between the conflicting visual sensations of value and hue. Which means your basic consideration, when thinking about color saturation, is how to strike the balance between value and hue.

What is value good for? As the dominant visual information our vision extracts from light, value is essential to show the spatial form of physical objects in the world represented by the painting. Value expresses the direction and intensity of light, the purity of the air, the volume, shape and spacing of objects.

Lights and darks are able to do this because they neither clash nor harmonize with actual reds, yellows, greens, blues and violets. Value stands behind color as an independent dimension. In fact, the traditional grisaille oil painting method turns this fact into a method: it blocks out the picture in tones of gray, then animates distinct surfaces with transparent glazes of color.

In contrast, hue functions primarily to show the quality of light and the inner composition of objects in the world  their molecular or crystal structure, fine grained surface texture, translucency, refractive qualities, and so on. Value signals that the orange and lemon both have shiny, textured skins; color signals their inner taste. A red and a brown apple have the same value, but we see (almost with our gut) that the brown apple won't be good to eat.

The problem for artists is that intense hues make it difficult to see values accurately: using saturated colors has the effect of weakening the value structure of a painting (making the relative value of colors more difficult to see). There is a deep design reason why modern artworks that emphasize expressive extremes of color also suppress the value and perspective cues of space, and why the older style of paintings emphasized chiaroscuro and landscape depth within a limited chromatic range. Chroma or saturation is not merely the balance between two academic colormaking attributes, but the boundary between two very different design approaches to the visual richness of the world.

This "black or blue" distinction is not neat, for three reasons. First, hue and value are linked in familiar ways: pine trees are green but also dark, lemons are yellow but also light. Second, our expectation under normal daylight is to see lighted surfaces as warm hues and dark surfaces or shadows as cool hues; hue seems aligned with the warm/cool color contrast. Finally, surfaces shift from primarily hue to primarily value depending on the illumination: in dim lighting all colors become varied shades of near gray, and in extremely bright lighting colors appear bleached or denatured.

The key to using dull or unsaturated passages of color is that dull colors can accent both value and hue. Because they are much closer to a pure gray than intense hues, near neutrals are easier to read as part of the value structure; they combine with pure values. Because they still contain hue information, they accent or contrast with pure hues. They increase each colormaking attribute, but through harmonious or antagonistic means.

This last effect, the antagonistic relationship between dull and intense hues, can be controlled by choosing near neutrals that are analogous or complementary hues to the saturated hues near them. The effects of simultaneous complementary contrast will cause saturated hues to appear more distinct but sometimes less resonant than they will against an achromatic background. Placing the same hues near to analogous near neutrals acts to diffuse their color power over the entire near neutral area.

These points will become clearer in the examples below, and once you actually experiment with near neutrals in visual design. The point is that near neutrals are important, no matter what your style of painting. Using these dull mixtures effectively means coming to grips with the three value painting challenges  seeing neutrals accurately as values, mixing them as hues accurately, and effectively using their combined value and hue in visual design.

near neutrals and color design

Let's start with the use of near neutrals in color design. This is the way the subject is normally approached, and basic design effects provide a good context for other problems, such as seeing the hue bias of a near neutral accurately.

Students are commonly taught the importance of simultaneous complementary contrast in color design. However, important effects also arise from simultaneous analogous contrast, in which the background color is not the complementary hue of the saturated color, but the same or similar hue.

Some visual examples will illustrate the main points. Again: the visual impact of color samples on a light transmitting computer monitor will not be the same as the visual effect of light reflecting paints on paper. Treat these examples as illustrative.

First we consider saturated color samples from the twelve tertiary points of the visual color wheel, displayed against a constant achromatic mid value background (example 1). Because the lightness of highest chroma color varies by hue, so the central colors are not of equal lightness and chroma, though each hue is shown at the highest lightness that retains the maximum saturation. (In all the examples in this section, the central colors are arranged vertically as visual complementary pairs.)

Nothing surprising here. The gray backgrounds seem to vary slightly, because of the complementary color shifts produced by the intense hues (as explained in the section on complementary color contrast). The saturated colors all appear very lively, and many seem to stand in front of the gray background (with the possible exception of the purple and red blues, which are darker in value than the gray).

Now, let's try to fire up the central colors by changing the background grays to a complementary near neutral color (example 2). Again, the background is darker valued than all the central colors except for the purple (top left) and blue violet (bottom right).

Your mileage may vary, but I don't see a tremendous difference in the quality of the saturated central color patches (compare examples 1 and 2). If anything, the "advancing" effect of the bright colors is accented (now even the purple and blue violet seem to stand in front of their backgrounds), and this enhanced color contrast seems to be the chief design impact: complementary contrast separates colors in a pattern. The background colors have been altered in the same direction that a simultaneous complementary contrast would shift them, so we have slightly intensified the color contrast without altering its character.

Now let's use the same central patches and backgrounds as before, but flip the background colors vertically, so that each saturated hue is now seen against an analogous near neutral  that is, its own hue but at lower saturation (example 3).

The difference in the color effect is striking (compare examples 2 and 3). Now the saturated hue seems to expand or diffuse into the dull background, uniting with it in a quality of shared glow or influence, but not a chromatic quality so much as a unity of mood or light. The metaphor of light seems justified by the significant apparent shifts in value and color temperature that occur in some background colors  the warm color backgrounds in particular  and the apparent chroma increase in the backgrounds, producing an illusion of greater hue differences from one background to the next. Yet the sense of color harmony seems greater across the example as a whole.

If you compare the dull backgrounds in the previous two figures (backgrounds that are exactly the same, just placed around different saturated colors), you will see that the effect on the dull colors is very noticeable. In effect, analogous dull colors act as color resonators, vibrating in harmony with their more intense color neighbors and gaining in apparent saturation as a result.

These backgrounds were set to a constant mid value, which makes them darker than all but two of the central saturated squares. What happens when the dull background colors are generally light valued and often lighter than the saturated central colors (example 4)?

In this example the backgrounds are lighter valued than all the saturated colors except yellow (top right), and the greens and blue greens (bottom left 4 samples).

Here the results are mixed. For the very light valued greens and blue greens, the background is of a very similar value but not lighter, so the difference in chroma between the background and central square is interpreted as an increase in luminosity, and the central colors appear brighter. For the central squares that are darker valued than their backgrounds, the simultaneous lightness contrast causes them to appear even darker, and this darkening has an apparent effect on the chroma as well, making the colors appear duller. As a result, the dark warm hues function less effectively as color accents, and the light cool hues more effectively, when placed within light valued complementary contrasts.

Now let's flip the backgrounds again (example 5). The yellow, greens and blue green are still lighter valued than their backgrounds.

Now all the saturated colors are slightly enhanced, and the backgrounds are brightened even more: the whole array appears more luminous, and every color (central squares and backgrounds alike) has a richer, warmer presence. This is especially apparent in the darker central colors, where the strong lightness contrast is softened by the analogous hue relationship.

The comparisons so far indicate that lightness and chroma contrasts have different effects, depending on hue. The lightness contrast is negligible for the saturated green and blue green hues, but very strong for the saturated warm hues and reddish blue. Red and red orange (top row, center two squares) appear especially affected.

I said earlier that this is because the lightness of the maximum saturated color varies from one hue to the next. We can explore this relationship further by making the background color the same lightness as the central square, with the background either a complementary hue (example 6) or an analogous hue (example 7).

Comparison of these examples with each other suggests that the chroma and hue shifts for both saturated and near neutral colors have been minimized. This reduced contrast is also apparent when these examples are compared to earlier examples with dark backgrounds of identical lightness (examples 1-3). (To compare with earlier examples, open this page in side by side browser windows, and align the examples you want to compare in each window.)

In other words, simultaneous color contrasts are minimized in colors of equal lightness. Of course, part of this contrast reduction is due to the greater variation in lightness across the whole array of colors: central colors are "merged" with their backgrounds to accentuate the lightness differences across the backgrounds. But we notice too that complementary color contrasts do not produce any significant hue shifts in the central squares, and analogous backgrounds have lost almost all their resonance (indeed, the yellow green at lower left seems to disappear into its analogous background). Lacking any value contrast to start with, color vision is not stimulated to accent the contrasts on hue or chroma.

Finally, we can minimize the differences between central squares and backgrounds on both value and chroma to see how hue contrasts work for "average" (moderately saturated, mid valued) color samples. Here are the color examples again, with complementary color backgrounds (example 8) and with analogous color backgrounds (example 9).

Several things seem to be happening at once. First, the relationship between lightness and chroma across different hues means that once we fix the lightness of the central squares to a single value, some hues will appear lighter or darker than others based on chroma differences alone. Thus, the hues that have the highest chroma at mid to low values (blue violet, far right in bottom row, or red and orange, middle of top row) appear relatively bright, but the hues that have the highest chroma at high values (yellow, far right of top row, and greens, middle and left of bottom row) have their chroma reduced by the darker value and appear relatively dull. These are not color shifts due to contrast effects, but are inherent to the chroma/lightness relationship of each hue, and are inescapable when we try to compare effects across different hues.

That said, the complementary color contrast causes all the moderately saturated color swatches to appear relatively more distinct. By comparison, the yellow, green and blue green central squares are almost lost against their analogous color backgrounds, although all hues are more "merged" with their analogous backgrounds, as they are so similar in value. Once again, complementary color contrast serves primarily not to enhance individual hues, as "color theory" likes to put it, but to clarify visual textures or patterns among moderately saturated and dull colors.

Third, because the value contrasts have been minimized, the chroma and hue shifts are reduced as well. Even so, the near neutral backgrounds seem to receive a larger hue and value shift from the contrast than the moderately saturated colors. In general, colors with higher chroma induce shifts rather than receive them. This effect seems to hold true, even when the most saturated colors are only moderately high in chroma.

Many more examples could be added to demonstrate the interactions or mutual effects among hue, value and chroma. At this point it will be most useful for you to repeat these effects, using either colored construction or origami papers, or squares painted with watercolors. The most important design principles we can take away from the present examples include the following:

 The size of color shifts depends primarily on the value contrast between color areas. Value acts as the determinant of other shifts: where value contrasts are large, hue and chroma differences are muted; where value contrasts are small, chroma shifts are accented. (For discussion of the relative power of value, chroma and hue in simultaneous color contrasts, see the section on simultaneous color contrasts.)

 Light valued backgrounds are more powerful than dark valued backgrounds. In general, when there is already a strong chroma contrast between two color areas, a light colored near neutral area is interpreted by color vision as if it were information about the illuminant, and this "illuminant" color affects nearby saturated colors in the same way colored lighting would (enhancing analogous hues, and neutralizing complementary hues). The chroma enhancing effect of analogous, light valued backgrounds is greatest for mid to light valued saturated colors; dark valued saturated colors will appear darker and duller, as if they were interpreted as shadows rather than the illumninant.

 Lightness or chroma contrasts vary by hue. We found that light valued near neutral backgrounds produced the strongest effect of enhanced luminosity in the saturated hues that were also light valued  yellow, greens and blue greens. Dark valued near neutrals produce a similar effect for dark valued saturated hues. Roughly, when value differences are very small, chroma differences enhance apparent chroma; when value differences are very large, chroma differences affect apparent value.

 Analogous and complementary contrasts have different effects. Complementary color contrasts serve to separate unrelated color areas in patterns or complex visual textures, especially when all colors are moderately saturated. Analogous color contrasts serve to unite unrelated color areas and reinforce their common hue by an apparent increase in saturation, especially when the lighter valued colors are unsaturated.

 Analogous relations are more powerful than complementary relations. The analogous, light valued near neutral backgrounds combine with the saturated colors to suggest a colored illuminant, strongly enhancing the sense of color richness and color unity.

 Near neutrals show greater apparent shifts. All other things equal, the near neutral background shows a larger color shift induced by the saturated color than the saturated color shows a shift caused by the near neutral background. This shift is greater for analogous than complementary colors, and is greater for lighter valued colors.

As I've already suggested, these general principles are less effective than actual experience with color mixing. It turns out this is also true when we look at an even simpler problem: recognizing color values accurately.

seeing color value

There are two challenges to seeing near neutral colors accurately: identifying the color value (on a value scale), which we'll look at now; and identifying the hue bias in dull or near neutral color, discussed in the next section.

Our natural tendency is to take a one problem/one solution approach to life, but the problem of recognizing color values is not an easy one to solve.

A standard trick is to "squint" or narrow your eyelids when looking at a landscape or still life, which supposedly helps you to see the values more clearly. In a way it does, because it reduces the overall luminosity of the visual field, which in turn lowers the apparent chroma of all the colors  and colors lower in chroma are easier to read as pure values.

Another trick is to carry three slide frames fitted with red, green and blue filters or colored cellophane. Each transparency will cause the hues similar to it to appear at their natural values, and all other hues to appear darker and closer to gray. The green filter is especially effective, since it is neither warm nor cool, and so cancels out the effects of color temperature. Using all the filters, one after another, will help you to separate color values from the effects of hue and chroma.

All these tricks are more useful in analyzing the actual values of the motif or subject you are painting. I feel the best approach for learning the value of color mixtures is to use the artist's value wheel to select a triad of similarly valued paints (green gold, orange and turquoise for light valued paints, quinacridone carmine, phthalo green BS and cobalt blue deep for dark valued paints, etc.), and mix color circles of similar value. The illustration shows four of these triad circles, and below them the same images in a pure gray scale.

color circles made of similar valued triads

This approach has one great merit: it helps you to learn the standard value for each hue you use, without guesswork. The artist's color wheel is based on spectrophotometric color measurements of paint pigments across several different brands of watercolors, so the values assigned to pigments are highly reliable. No guesswork is involved.

An added benefit is that, with minor variations, the mixtures of any equal valued colors you chose for a color circle will have the same value as the pure pigments. You also learn the characteristic value of a range of color mixtures  green gold with turquoise, carmine with phthalo green.

The final aid is, of course, the value scale. Some painters suggest you make such a scale yourself, through successive layers of dark or black paint. I strongly recommend you buy a standard photographer's gray scale (for example as manufactured by Kodak), sold in any good camera store or photographic supply store. The merit is that these gray samples are accurate, and have a dull glossy finish that appears relatively constant across a wide range of illumination. To use the gray scale, simply hold it alongside the color area you want to evaluate; you can also use a paper punch to put small holes along the inner edge of each gray swatch, and look at the color through these holes (this eliminates the visually confusing effects of contrast colors near the area you want to evaluate).

What do these various tricks or tools amount to? Nothing more than patient, trial and error learning. Some artists are naturally endowed with a light sensitive eye. For the rest of us, seeing values accurately is a very complex visual skill that requires long and patient practice.

The advantage of using the artist's color wheel, or colored filters, is that you apply a consistent method to many different color samples (in paints or the real world). They key to relatively painless learning is to create these consistent methods and use them in many different situations.

seeing hue bias

Finding the hue bias in a dull or near neutral color is another subtle problem in color perception. The problem is made more difficult because it is hard to find near neutral color samples with which to train one's color eye.

The near neutral color samples in this section are meant to be illustrative only. I recommend that you buy an inexpensive color atlas, such as the The New Munsell Student Color Set or the Process Color Manual, to assist you in recognizing and distinguishing among greens, reds, yellows or blues that are very close to gray.

One approach to hue discrimination might be to start with the saturated color circle, with its complete color range, and look at color samples of decreasing chroma or saturation at constant value, to see what a dull blue or a dull red looks like.

a palette of near neutrals (CIELAB L = 65)

We first notice that the different hues are harder to distinguish as near neutrals than as saturated colors. The hue gradations seem to melt away as the samples shift toward lower chroma.

The hue fading effect varies by hue: the turquoise and greenish blue samples appear bright around a chroma of 35, while the samples of yellow or yellowish green appear dull. At different lightness values than the CIELAB L of 65 chosen for this example, other colors would appear more intense at a chroma of 35. So the hue fading depends both on the hue and the value we are considering.

With those basic cautions in mind, let's start with a pure achromatic hue and work outwards. This is closer to the actual situation you face when painting, which is identifying a near neutral hue without a strong hue near it to aid in recognition.

the circle of grays

The circle of grays starts with a pure achromatic sample of lightness 50. It is surrounded on four sides by samples at a chroma of 4, then at a chroma of 7 at lightnesses of 50 and 80. The color samples around the circumference identify the hue along each "spoke" of the circle.

Working outwards in this way, it's obvious that our color categories have broken down: we can't distinguish among these grays with the same precision that we can distinguish among the colors in the outer circle. We need to learn a new hue circle, an near neutral hue circle, as our framework for identifying near neutral colors.

Part of the problem is that we must have new color terms to talk about the differences among the grays. The hue terms we use for the saturated colors just don't apply. There is a very obvious difference between the red violet and blue violet, but the corresponding grays look pretty much the same. What should we call this dull color?

To find an answer, try to divide the grays in the outer or middle circle into groups of similar grays. How many groups do you come up with? How sure of the groups are you?

There are little or no differences among the samples of chroma 4. Differences might become apparent, through color contrast effects, if these samples were placed next to more intense color samples. At chroma 7, there does seem to be a difference between "warm" colors (magenta through yellow) which appear as a dull brown, and "cool" colors (green through blue) which all seem to be a dull green. At a lighter value (L=80), this contrast is more obvious, and the violets (red violet to blue violet) seem also to form a distinct grouping.

These groups seem roughly to correspond to the three additive primaries of scarlet, green and blue violet. It seems that color vision cannot achieve a reliable hue recognition because the outputs from the R, G and B cones are so nearly equal; but it can at least recognize which of the three cones is responding most strongly. The hue separation becomes clearer at lighter values, because at this value all the cones are much more active, so the slight differences between them become magnified.

the circle of grays (hue symbols omitted)

If we look at samples with a chroma of 14, the hue differences are distinct for each hue at a lightness of 90, and are more distinct at a lightness of 50. The warm colors and green blues/blue greens still seem to form two large clusters, but the hue transitions from orange to green and from blue to magenta are more distinct. Increasing the chroma further unfolds hue differences at darker and darker values  depending on which hue we are looking at.

These comparisons suggest the following method for identifying the hue of near neutral colors, whether in mixed paints or in the surfaces of the real world:

1. Warm or cool? As we've seen, this is the most robust color judgment, even in near neutral colors. If you cannot make this basic distinction, then the color is either a true neutral, or it is a very dull green or violet.

With paints, lightening the color mixture with white paint or water can assist in color identification, as this brings the luminosity up the point where reliable hue differences appear even at very low chroma. On natural surfaces, look at the surface area that is most strongly illuminated. (If the reflected light is dazzling, look at areas that are illuminated indirectly.)

2. Closest anchor. Proceed to narrow down the location of the color by choosing between the widest possible hue alternatives. If it is a warm color, ask yourself if it is closer to yellow or magenta; if a cool color, whether it is closer to turquoise or blue violet. Then continue dividing the color alternatives by halves: if you decide it is closer to yellow, then ask whether it is closer to yellow or orange; if orange, whether closer to orange or deep yellow? Stop when the hue choice seems arbitrary or uncertain.

3. Saturation. You've located the hue; the difficulty in making that judgment gives you a sense for the color's chroma or intensity. Try to imagine a gray and the purest imaginary hue of the same value, and locate the color in your imagination between these two extremes.

4. Adjacent color. Once you have made as specific a hue recognition as possible, consider the contrast effects induced by adjacent colors. A greenish gray next to a magenta will appear less saturated and darker than it would appear in isolation; the same gray next to a blue green will appear more saturated and lighter. Hue shifts will also be present.

5. Value. You identify the value of the hue last of all, because the apparent value of colors varies by hue, and you may need to adjust for this mentally when determining your color mixture.

6. Range of Values. The last step to consider the place of the color value in the overall value structure of the image. This is also related to the visual environment in which you are trying to make the color judgment. Is the lighting strong, or weak? Are your eyes somewhat blinded by light, or is the surface darkly shaded? In dim light you may want to make values lighter than they seem; in bright light you may want to paint the colors less saturated than you would normally. (Some of these issues are explained at the page on light in the world, and at the page on value design.)

I emphasize again that learning to recognize and then mix near neutral hues is a slow process. It goes hand in hand with your color mixing skills, your knowledge of the effects of light and color contrast on color judgments, and your experience in making paintings.

mixing complementary paints

Any three paints that define a mixing triangle which encloses the center or neutral point of the color wheel can create a perfect gray if mixed in the right proportions.

There are also many combinations of two paints that can mix a neutral or gray tone. These are subtractive complementary colors, or mixing complements. These color combinations are both convenient (two paints are easier to work with than three) and effective (two paints can often mix a darker neutral than three). Most artists memorize the important combinations as part of their color mixing lore.

I learned over my first few years of teaching myself to paint that much of the currently available information about mixing complements in watercolor paints is inaccurate or incomplete. Sometimes the errors are trivial and sometimes they are large.

Because your mixing intuitions depend on your knowledge of mixing complements, I will go into this topic in depth. (Is there any other way?)

I approached this problem methodically, and an explanation of my test methods, with a complete listing of test results, are provided on this page. The image at right, which shows the mixing complementary tests for ultramarine blue (PB29), shows the gist. Each line connects the measured color locations of ultramarine blue mixed with every warm pigment between cadmium yellow deep and cadmium scarlet. Any mixture that passes within the light gray circle has a minimum chroma of 5 or less, which is to most viewers indistinguishable from a "pure" gray; any mixture that passes within the dark gray circle has a chroma of 2 or less and really is a pure gray. (At least, watercolors marketed as white, gray or black have a chroma within that range.) Three lines fall within this circle: raw umber, quinacridone gold, and benzimidazolone orange.

The chart below shows all the mixing complements between warm and cool watercolor pigments (from ultramarine violet BS to chromium oxide green). (Again, this page presents the same information as a table. I've organized the table around the blue and green pigments, because there are fewer of them.)

near neutral mixing linesfor ultramarine blue

the watercolorist's mixing complementspigments that make "pure gray" mixtures are joined by dark lines, "near gray" mixtures by light lines; see this page for the same information in tabular form

Before you panic: this diagram is meant to make a single point. If the hue relationships between mixing complementary colors were consistent, then the lines connecting them would not cross each other. As cool hues become greener, their mixing complements should become bluer, so lines between them would stay roughly parallel all the way down the chart. This is obviously not the case!

 Nearly all the mixing complements for blues and blue greens are limited to the warm colors from carmine to deep yellow. That is, most mixing complements lie around the warm/cool color contrast, which is really the "mother of complementaries." This is emphasized by the way the mixing lines tend to slant toward the red orange center of the warm color range (around burnt sienna).

 With few exceptions (yellow ochre and other dull deep yellows), yellow has no role as a mixing complement. This is because yellow reflects both "red" and "green" light, and it is extremely difficult to get a reddish blue or blue violet color that can exactly cancel out both parts of the spectrum equally.

Is Stephen Quiller incorrect to say that ultramarine violet and lemon yellow make a pure gray mixture? Yes. The bluish shade of ultramarine violet (PV15) he recommends (made by M. Graham or Blockx) produces a cadaverous near gray with any yellow hue  lemon yellow through deep yellow. But these mixtures are actually a greenish gray, not a true gray. They appear gray, however, because we tend to choose a cool color as a "true" gray. I used a spectrophotometer to measure my test mixtures; Quiller used his eyes.

 The warm hue mixing complements for most blue or green pigments cover a large hue span. This means that paint mixing cannot identify unique complementary colors for any blue or green. Take phthalo green BS (PG7) for example: you can get a dead on dark gray by mixing it with pyrrole scarlet (PR255) or with perylene maroon (PR179). So is the "true" complementary color for phthalo green a bright scarlet or a dull carmine? (Quiller pairs phthalo green BS with quinacridone rose PV19, which produces a violet mixture with a minimum chroma of around 12.)

 Some of the mixing complements contradict color wheel logic. Compare, for example, the mixing complements of prussian blue (PB27) and phthalo turquoise (PB16). The perfect mixing complement for prussian blue is venetian red (PR101), and the best complement for phthalo turquoise is perinone orange (PO43). But phthalo turquoise is much closer to green than prussian blue, and perinone orange is also closer to green than venetian red: as the blue hue moves counterclockwise around the color wheel, the complementary color moves clockwise! You just can't get that to make sense on a color wheel.

The truth is that you can't show mixing complements as a color wheel. No matter how you tug and pluck, you can't unravel the mess created by the substance uncertainty of real paints. The only way to cut through the knot is to work with the color relationships defined by additive color mixing, as I've done with my artist's color wheel, and learn the mixing complementary relationships by rote for the paints actually on your palette. Paints you don't use you don't have to know about.

the material qualities of paint

I've carried the color mixing exercise to an unartistic extreme. But I urge you to verify the results, at least for paints on your palette, for a very different reason. Mixing up your own complementary paint combinations is a splendid way to learn the subtle material attributes of the pigments and paints you use.

A really unfortunate (and unintended) outcome of learning "color theory" is the prejudice that paints are "colors" only. This is very much like thinking of flowers as "colors." Skillful gardeners and flower artists, when they plan garden beds or flower arrangements, also think of the size and shape of the plants, the shape and spread of blossoms, the arc and twist of stems, and the pattern and sheen of leaves. As a painter, you need to understand the physical, handling and appearance attributes of each paint or pigment you use, not just its "color." Choosing paints to create harmonious visual effects other than color is one of the hallmarks of an accomplished watercolor artist.

The benefit of near neutral mixtures is that color is eliminated almost entirely, so paint value and texture is all there is to look at. Paints that you thought of as "blue" or "dark" now impress you with textures and surfaces all their own. You can see clearly the subtle harmonies or difficulties created by mixing different types of pigments.

Here is a summary of some of the notes I made while testing neutral mixtures:

 Mixtures of two synthetic organic pigments  a phthalocyanine with a pyrrole, for example  give the strongest, cleanest, most homogenous grays. These mixtures can produce extremely even color areas and exceptionally dark grays (in some cases even darker than ivory or carbon black), with the drawback that they make visually boring and somewhat dull surfaces across large areas.

 Mixtures of the cool phthalocyanines with a warm iron oxide (earth) pigment are generally very smooth, with a slight granularity that lends the finished color a velvety visual texture. (As always, you must apply the color decisively and not fuss with it as it dries; this dulls the surface and produces "mud.") Mixtures with red iron oxide (venetian red, light red, indian red) must be fairly diluted, however, because those earth pigments are thick and opaque, which can cause a dense mixture to streak when brushed on.

 Burnt sienna (PBr7) and venetian red (PR101) are the two workhorse pigments for neutralizing colors, but a dark raw umber (PBr7) is also often useful for reddish blue paints.

 The very pure gray that results from venetian red with iron (prussian) blue (PB27) is "Homer's gray." It was used with special grace by Winslow Homer to capture the dark stormy gray skies of Cullercoats and Bermuda.

 Mixtures of phthalocyanine blue or green with cadmium pigments can be very confusing to work with. The finer cadmium particles have a tendency to float on the surface of the mixture, which confuses your perception of the color; you have to look through this surface to the color of the inner solution as you brush it out against the white palette. Make test swatches to confirm the dried color appearance before applying to the painting.

 Mixtures of cobalt blue or cobalt turquoise with an iron oxide (earth) or synthetic organic pigment (the quinacridones in particular) are especially beautiful. (The exception is cerulean blue, which turns out unusually dull when mixed with the earth pigments.) Cobalt pigment particles are just large enough to create a distinct stippled or speckled texture to the dried color, which causes the separate pigments to appear as two interlaced colors rather than a single homogenous hue. This color contrast is especially intense with a scarlet and turquoise, or magenta and green paint, and is strongest in middle grays (moderately diluted mixtures).

 The gray that results from ultramarine blue (PB29) and burnt sienna is one of the most evocative and texturally interesting grays. It is slightly biased toward red, which gives it a fundamental warmth even in its most neutral tone, and the textural effects that result from the wet in wet application of the two pigments, which have a strong tendency to separate in juicy washes, can be startlingly lovely.

 Grays are especially hard to mix because the margin of error is limited in all directions. In most mixtures it does not really matter if your finished color is slightly off hue from the color you wanted; the color still takes on its desired role. But a gray that varies in any direction from the exact color you want to mix is no longer a gray, and may even shift temperature from warm to cool. This problem arises because of the drying shifts of the complementary pair: a mixture that looks spot on when wet will often dry with a hue bias. It's best to paint a test swatch of any gray mixture  and let it dry for at least 10 minutes  to be sure of the finished color. Drying shifts arise in various ways: with dark blue pigments  ultramarine blue, indanthrone blue and phthalo blue  because they have very large drying shifts in lightness and saturation; with cobalt pigments, because they lose tinting strength in a mixture as they dry. An exception is dioxazine violet with sap green: both paints individually have large drying shifts, but the size and direction of the shifts tend to cancel each other out, leaving the finished neutral color pretty much as you mixed it.

As these comments suggest, mixing near neutral colors present slightly different mixing problems than you encounter when mixing more saturated colors at the outer edges of the color wheel. But these problems can help you learn the essential nature of the paints and pigments more clearly.